Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently,

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Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?

A) 3%
B) 6%
C) 12%
D) 20%
E) 24%



OA C

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The shelf can accommodate 25 books
20% of the shelf spots remain
Total books on the shelf = (100 - 20)% * 25
= 80% * 25 = 20
Let the total number of Chemistry books = x
Total number of Physics books = x + 4
Since the total no. of books = 20
Then, x + (x+6) + [12 (x+4)] = 20
2x + 4 + 2x + 8 = 20
4x + 12 = 20
Chemistry books = 2, Physics books = 6 and Mathematics books = 12
Probability of picking Mathematics book = 12/20
Probability of picking Chemistry book = 12/20
The exact order of picking the books is not known. So, for the total probability, we will estimate the sum of the following of the probability of picking Mathematics first or picking Chemistry first.

$$=\left(\frac{12}{20}\cdot\frac{2}{20}\right)+\left(\frac{2}{20}+\frac{12}{20}\right)=\frac{6}{100}+\frac{6}{100}=\frac{12}{100}$$
$$=12\%\ \ \ \ \ \ \ \ \ \ \left(Answer\ =\ option\ C\right)$$

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BTGmoderatorDC wrote:
Tue Mar 16, 2021 6:49 pm
Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?

A) 3%
B) 6%
C) 12%
D) 20%
E) 24%



OA C

Solution:

Since 20% of the shelf is empty, 80% is full and thus, there are 25 x 0.8 = 20 books on the shelf.

Let c denote the number of chemistry books. Then, there are c + 4 physics books and 2(c + 4) = 2c + 8 mathematics books. Since the sum of the books on the three subjects is 20, we have:

c + (c + 4) + (2c + 8) = 20

4c + 12 = 20

4c = 8

c = 2

Thus, there are 2 chemistry books, c + 4 = 6 physics books and 2c + 8 = 12 mathematics books.

The probability that Richardo reads a mathematics books in the library and checks out a chemistry book is 12/20 x 2/20 = 24/400 = 6/100. The probability that he reads a chemistry book in the library and checks out a mathematics book is also 2/20 x 12/20 = 6/100. Thus, the probability that one mathematics and one chemistry book is read is 6/100 + 6/100 = 12/100 = 12%.

Answer: C

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